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values | ground_truth_solution stringclasses 177
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Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A straight, symmetrical railway embankment has a bottom width of \\(a\\) and a top width of \\(b\\), with a height of \\(m\\). A road is being built that runs perpendicular to the axis of the embankment. The embankment is cut all the w... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Monk is a multi-talented person, and prepares results for his college in his free time. (Yes, he is ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. If the equation $m x^{2}-2(m+2) x+m+5=0$ has no real roots, then how many real roots does the equation $(m-5) x^{2}-2(m+2) x+m=0$ have?\n(A) 2 \n(B) 1 \n(C) 0 \n(D) Uncertain"
},
{
"from": "assistant",
"value": "<|begin_of_... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. On a table, there are 10 cards numbered $1, 1, 2, 2, 3, 3, 4, 4, 5, 5$. These 10 cards are shuffled and arranged in a row from left to right. Then, the number of cards between the two 1s, the two 2s, the two 3s, the two 4s, and the two... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. P is a fixed point in the plane. Show that amongst triangles ABC such that PA = 3, PB = 5, PC = 7, those with the largest perimeter have P as incenter."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Jeffrey stands on a straight horizontal bridge that measures $20000$ meters across. He wishes to place a pole vertically at the center of the bridge so that the sum of the distances from the top of the pole to the two ends of the bri... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let the quadratic function $f(x) = ax^2 + bx + c$. When $x = 3$, it has a maximum value of 10, and the length of the segment it intercepts on the x-axis is 4. Then $f(5) = \\ \\quad$ ."
},
{
"from": "assistant",
"value": "<... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given an isosceles triangle, find the set of points inside the triangle such that the distance from these points to the base is equal to the geometric mean of their distances to the lateral sides."
},
{
"from": "assistant",
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a cube \\(ABCD A_1 B_1 C_1 D_1\\) with edge \\(a\\). Point \\(E\\) is the midpoint of edge \\(AD\\). Vertices \\(M\\) and \\(N\\) of a regular tetrahedron \\(MNPQ\\) lie on the line \\(ED_1\\), and vertices \\(P\\) and \\(Q\\) li... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In the isosceles trapezoid \\(ABCD\\), where \\(AB\\) is parallel to \\(DC\\), \\(AB = 998\\), \\(DC = 1001\\), and \\(AD = 1999\\), point \\(P\\) is on segment \\(AD\\). The number of points \\(P\\) that satisfy the condition \\(\\ang... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the dividend if each asterisk (*) in the given long division indicates a certain digit."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out this long division problem. So, the pr... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. How many zeroes does the product of \\( 25^{5} \\), \\( 150^{4} \\), and \\( 2008^{3} \\) end with?\n(A) 5\n(B) 9\n(C) 10\n(D) 12\n(E) 13"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's try to figur... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given \\( n \\) (\\( n \\geq 4 \\)) points \\( A_1, A_2, \\ldots, A_n \\) in a plane, with no three points being collinear, and each point is connected to at least 3 other points by line segments, prove that there exist \\( 2k \\) dist... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A person brought 1000 dollars in one-dollar bills and 10 empty bags to a bank. He asked the clerk to distribute the money into the bags in such a way that, whenever he needs any amount of money, the clerk can give him the required sum ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the set \\( A = \\{ a \\mid -1 \\leqslant a \\leqslant 2 \\} \\), find the area of the plane region \\( B = \\{ (x, y) \\mid x, y \\in A, x + y \\geqslant 0 \\} \\)."
},
{
"from": "assistant",
"value": "<|begin_of_tho... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Two circles intersect at points $A$ and $B$. Through these points, two chords are drawn in arbitrary directions, intersecting the first circle at points $C$ and $D$, and the second circle at points $C^{\\prime}$ and $D^{\\prime}$. Show... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.In this Kata, we will check if a string contains consecutive letters as they appear in the English alphabet and if each letter occurs only on... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. How many rectangles are there whose four vertices are points on this grid? [asy]\nsize(50);\ndot((0,0));\ndot((5,0));\ndot((10,0));\ndot((0,5));\ndot((0,10));\ndot((5,5));\ndot((5,10));\ndot((10,5));\ndot((10,10));\n[/asy]"
},
{
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. When processing numerical data, it is often necessary to calculate the arithmetic mean\n\n$$\nS(x, y) = \\frac{x + y}{2}\n$$\n\nand solve equations that involve the arithmetic mean. Find all finite (consisting of a finite number of ele... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Range Min of Max Query\n\nGiven a sequence of integer pairs (a_1, b_1), (a_2, b_2), .., (a_N, b_N).\... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In how many ways can the digits from 1 to 9 be placed instead of letters, so that all the resulting equations hold true?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how many wa... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Solve the inequality\n\\[|x - 1| + |x + 2| < 5.\\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I have this inequality to solve: |x - 1| + |x + 2| < 5. Hmm, absolute values can sometimes be tricky, ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In how many ways can the numbers from 1 to 100 be arranged in a $2 \\times 50$ rectangle such that every pair of consecutive numbers (numbers differing by 1) are always in cells with a common side?"
},
{
"from": "assistant",
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A greyhound race included 36 dogs. The number of dogs that finished before Punta was four times smaller than the number of dogs that finished after him.\n\nWhat place did Punta finish in?"
},
{
"from": "assistant",
"value":... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. An equilateral triangle with side length \\(a\\) rotates around an axis passing through its vertex and forming an angle \\(\\varphi\\) with one side. Find the volume \\(V\\) and surface area \\(S\\) of the resulting solid of revolution... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given a string str of length n, find if the string is K-Palindrome or not. A k-palindrome string tra... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Two people, $A$ and $B$, must get from point $M$ to point $N$, which is 15 km from $M$, as quickly as possible. They can walk at a speed of 6 km/h. Additionally, they have a bicycle that can be ridden at a speed of 15 km/h. $A$ starts ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. One endpoint of the major axis and one of the minor axis of an ellipse is $A$ and $B$, respectively, and one of its foci closer to $A$ is $F$. At which position of the point $M$ moving along the arc $A B$ will the area of triangle $M B... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Three similar triangles \\(PAB\\), \\(AQB\\), and \\(ABR\\) are constructed on the same side of line segment \\(AB\\). Similarly, three similar triangles \\(P'AB\\), \\(A Q'B\\), and \\(ABR'\\) are constructed symmetrically about the p... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Number $a$ is such that $\\forall a_1, a_2, a_3, a_4 \\in \\mathbb{R}$ , there are integers $k_1, k_2, k_3, k_4$ such that $\\sum_{1 \\leq i < j \\leq 4} ((a_i - k_i) - (a_j - k_j))^2 \\leq a$ . Find the minimum of $a$ ."
},
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a concert, 20 singers will perform. For each singer, there is a (possibly empty) set of other singers such that he wishes to perform later than all the singers from that set. Can it happen that there are exactly 2010 orders of the s... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Problem. The sum of two consecutive squares can be a square; for instance $3^2 + 4^2 = 5^2$ .\n\n(a) Prove that the sum of $m$ consecutive squares cannot be a square for $m \\in \\{3, 4, 5, 6\\}$ .\n(b) Find an example of eleven co... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find all polynomials \\( P(x) \\) that satisfy the identity\n\n\\[ \nx P(x-1) \\equiv (x-2) P(x), \\quad x \\in \\mathbf{R}\n\\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find all polyn... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. When you simplify $\\sqrt[3]{24a^4b^6c^{11}}$, what is the sum of the exponents of the variables that are outside the radical?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out how ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "I'm retiling my kitchen with different coloured tiles. In fact, it's going to have at least 2 colours - and 26 colours as a maximum.\nBut, I'm fussy. I want this wall to look random, but sometimes random isn't random enough.\nSo, when I lay out my tiles, I don't want to have any ... | I'm retiling my kitchen with different coloured tiles. In fact, it's going to have at least 2 colours - and 26 colours as a maximum.
But, I'm fussy. I want this wall to look random, but sometimes random isn't random enough.
So, when I lay out my tiles, I don't want to have any the same colour next to each other in the ... | Okay, I need to solve this problem where I have to generate a tiling of a grid with certain colors, such that no two adjacent tiles (up, down, left, right) have the same color. Also, all N colors must be used, and every possible valid tiling must have a non-zero chance of being generated. Oh right, and it's code golf, ... | To solve this problem, we need to generate a grid of tiles such that no two adjacent tiles (horizontally or vertically) have the same color, and all given colors are used at least once. The solution must be able to generate any valid tiling with non-zero probability.
### Approach
1. **Input Handling**: Read the grid d... | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A prime number \\( p \\) is such that the number \\( p + 25 \\) is the seventh power of a prime number. What can \\( p \\) be? List all possible options."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, le... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Consider an isosceles triangle. let $R$ be the radius of its circumscribed circle and $r$ be the radius of its inscribed circle. Prove that the distance $d$ between the centers of these two circle is \\[ d=\\sqrt{R(R-2r)} \\]"
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The function \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) satisfies \\( f\\left(x^{2}\\right) f^{\\prime \\prime}(x) = f^{\\prime}(x) f^{\\prime}\\left(x^{2}\\right) \\) for all real \\( x \\). Given that \\( f(1) = 1 \\) and \\( f^... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Bessie the cow has just intercepted a text that Farmer John sent to Burger Queen! However, Bessie is... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A house and store were sold for $\\textdollar 12,000$ each. The house was sold at a loss of $20\\%$ of the cost, and the store at a gain of $20\\%$ of the cost. The entire transaction resulted in:\n$\\textbf{(A) \\ }\\text{no loss or g... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Consider the following game: Initially, there are \\( k \\) piles of stones \\( (k \\in \\mathbf{N}^*) \\). In pile \\( i \\), the number of stones is \\( n_i \\). Two players take turns to perform the operation of taking stones: each ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Prove that if all faces of a tetrahedron are equal to each other, then the opposite edges of the tetrahedron are pairwise equal."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to prove that if ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. An Englishman owned a piece of land in Russia. He knows that, in his usual units, the size of his land is two acres. The cost of the land is 500,000 rubles per hectare. It is known that 1 acre $= 4840$ square yards, 1 yard $= 0.9144$ m... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Expand the polynomial \\((a + b + c + d + 1)^N\\) (\\(N \\in \\mathbb{Z}_{+}\\)) and combine like terms to obtain 1001 terms, each of which includes positive integer powers of \\(a\\), \\(b\\), \\(c\\), and \\(d\\). Determine the value... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( a > 0 \\). The function \\( f(x) = x + \\frac{100}{x} \\) has a minimum value of \\( m_1 \\) on the interval \\( (0, a] \\) and a minimum value of \\( m_2 \\) on the interval \\( [a, +\\infty) \\). If \\( m_1 m_2 = 2020 \\), th... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Does a non-rectangular triangle inscribed in a circle with a radius of 1 exist, where the sum of the squares of the lengths of two sides is equal to 4?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so t... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a $2000 \\times 2000$ grid, each cell is filled with either 1 or -1. Given that the sum of all the numbers on the grid is non-negative, prove that it is possible to find 1000 rows and 1000 columns such that the sum of the numbers at... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Prove the inequality\n\n$$\n\\begin{gathered}\n\\frac{A+a+B+b}{A+a+B+b+c+r}+\\frac{B+b+C+c}{B+b+C+c+a+r} > \\frac{c+c+A+a}{C+c+A+a+b+r}\n\\end{gathered}\n$$\n\nwhere all letters represent positive numbers."
},
{
"from": "assist... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nFind the equation of the normal to the given curve at the point with abscissa $x_{0}$.\n\n$y=2x^{2}+3x-1, \\, x_{0}=-2$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let me try to figure out how to fi... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Miklós offers the following bet to Laci: \"I will pay you 1 Ft after every lottery draw in 1967 in which the 5 drawn lottery numbers do not include 3 consecutive numbers, if you pay me 100 Ft after every draw that includes at least 3 c... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( n \\) be a positive odd integer.\n\n1) Determine, as a function of \\( n \\), the largest integer \\( r \\) with the following property: for any real numbers \\( a_{1}, \\ldots, a_{n} \\), there exist \\( r \\) integers \\( 1 \... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. From point \\( S \\), three rays \\( a, b \\), and \\( c \\) emerge, which are not in the same plane. The plane determined by \\( c \\) and \\( b \\) is perpendicular to the plane determined by \\( c \\) and \\( a \\). Given the angle ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given \\( f(x) = ax^2 + bx + c \\), prove that \\( f(n) \\) is an integer for all integers \\( n \\) if and only if \\( 2a \\), \\( a + b \\), and \\( c \\) are all integers."
},
{
"from": "assistant",
"value": "<|begin_of_... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. My club has 25 members. In how many ways can I choose members to form a 4-person executive committee?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's tackle this problem. The question is: My club h... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given lines \\( l_{1}, l_{2}, \\ldots, l_{2n} \\) on a plane, all intersecting at one point. A flea sits at a certain point \\( M \\) on the plane and jumps over the line \\( l_{1} \\), landing at point \\( M_{1} \\), such that \\( M \... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. It is known that \\(a + b + c < 0\\) and that the equation \\(a x^2 + b x + c = 0\\) has no real roots. Determine the sign of the coefficient \\(c\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "How can plasma-based food processing be optimized to enhance food safety and quality while minimizing energy consumption and environmental impact?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how to optimize plasma-based f... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.### The Story:\nBob is working as a bus driver. However, he has become extremely popular amongst the city's residents. With so many passenger... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $n > 1$ be an integer. A rook stands on an infinite white checkerboard. With each move, it shifts exactly $n$ cells either vertically or horizontally, painting the $n$ cells it traverses black. After making several such moves, with... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Prove that if in a triangular pyramid the sum of the lengths of opposite edges is the same for any pair of such edges, then the vertices of this pyramid are the centers of four spheres, each pair of which touches the other."
},
{
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a $35 \\cdot 44$ grid, how many different rectangles (including squares) are there?\n(A) 36\n(B) 87\n(C) 72\n(D) 102"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, let's see. The question is asking ho... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Evaluate $\\left\\lceil3\\left(6-\\frac12\\right)\\right\\rceil$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to evaluate the expression ⎡3(6 - 1/2)⎤. Wait, first, let me make sure I underst... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a sequence \\(\\left\\{a_{n}\\right\\}\\) with the sum of the first \\(n\\) terms \\(S_{n}\\) satisfying the equation \\(S_{n} + a_{n} = \\frac{n-1}{n(n+1)}\\) for \\(n = 1, 2, \\cdots\\), find the general term \\(a_{n}\\)."
},... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nThe lines containing the legs of an isosceles trapezoid intersect at a right angle. Find the lengths of the sides of the trapezoid if its area is $12 \\text{ cm}^2$ and the height is $2 \\text{ cm}$."
},
{
"from": "assistant"... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Rishi likes to play with strings.Strings have been his passion since his childhood.One day in colleg... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Arrange the numbers $1, 2, 3, \\cdots, 37$ in a sequence $a_{1}, a_{2}, \\cdots, a_{37}$ such that $a_{1}=37$ and $a_{2}=1$. Ensure that the sum $a_{1}+a_{2}+\\cdots+a_{k}$ is divisible by $a_{k+1}$ for $k = 1, 2, \\cdots, 36$. Determi... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A sequence \\( a_{1}, a_{2}, a_{3} \\cdots \\) satisfies \\( a_{1}=1 \\) and \\( a_{n+1}=\\sqrt{a_{n}^{2}+\\frac{1}{a_{n}}} \\) for \\( n=1,2,3, \\cdots \\). Prove that there exists a positive number \\( \\alpha \\) such that \\( \\fra... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the number of positive integers $n$ between $1$ and $1000$ , inclusive, satisfying\n\\[ \\lfloor \\sqrt{n - 1} \\rfloor + 1 = \\left\\lfloor \\sqrt{n + \\sqrt{n} + 1}\\right\\rfloor\\]\nwhere $\\lfloor n \\rfloor$ denotes t... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a point \\( M \\) on the median \\( CM_3 \\) of triangle \\( ABC \\). Lines \\( AM \\) and \\( BM \\) are drawn through this point, intersecting sides \\( BC \\) and \\( AC \\) at points \\( A_1 \\) and \\( B_1 \\) respectively. ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the maximum and minimum values of the function:\n\n1) \\( z = x^{2} - y^{2} + 2a^{2} \\) in the circle \\( x^{2} + y^{2} \\leqslant a^{2} \\);\n\n2) \\( v = 2x^{3} + 4x^{2} + y^{2} - 2xy \\) in the closed region bounded by the lin... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. In a convex quadrilateral \\(ABCD\\), side \\(AB\\) is equal to diagonal \\(BD\\), \\(\\angle A=65^\\circ\\), \\(\\angle B=80^\\circ\\), and \\(\\angle C=75^\\circ\\). What is \\(\\angle CAD\\) (in degrees)?"
},
{
"from": "assi... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Suppose that $b$ is a positive integer greater than or equal to $2.$ When $197$ is converted to base $b$, the resulting representation has $4$ digits. What is the number of possible values for $b$?"
},
{
"from": "assistant",
... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Calculate the limit of the function:\n\n\\[\n\\lim_{x \\to 0} \\left( \\frac{\\sin 2x}{x} \\right)^{1+x}\n\\]"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the limit of (sin 2x / x)^(1... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "How do the effects of gravitational waves impact the internal structure and stability of a neutron star?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out how gravitational waves affect the internal structure and stability of a... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that \\(a\\) and \\(b\\) are positive integers and \\(c = \\frac{a^{a+1} + b^{b+1}}{a^a + b^b}\\), show that \\(c^a + c^b \\geq a^a + b^b\\) by considering \\(\\frac{x^n - n^n}{x - n}\\) or otherwise."
},
{
"from": "assis... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the integers \\( n \\) such that 6 divides \\( n-4 \\) and 10 divides \\( n-8 \\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find all integers n where 6 divides n - 4 and 10 divide... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A binary string is called *alternating* if no two adjacent characters of the string are equal. Forma... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Calculate the volume \\( V \\) of a sphere with radius \\( R \\) using a definite integral."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the volume of a sphere with radius R using a d... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There are two lists of different length. The first one consists of keys, the second one consists of values. Write a function ```createDict(ke... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. If \\(\\frac{99!}{101! - 99!} = \\frac{1}{n}\\), determine the value of \\(n\\)."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so I need to find the value of n such that 99! divided by (101! minus 99!) ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The distance between the centers of two non-intersecting circles is \\(a\\). Prove that the four points of intersection of the common external tangents with the common internal tangents lie on a single circle. Find the radius of this c... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $a$ , $b$ , $c$ , $d$ be complex numbers satisfying\n\\begin{align*}\n 5 &= a+b+c+d \n 125 &= (5-a)^4 + (5-b)^4 + (5-c)^4 + (5-d)^4 \n 1205 &= (a+b)^4 + (b+c)^4 + (c+d)^4 + (d+a)^4 + (a+c)^4 + (b+d)^4 \n 25 &= a^4+b^4+c^4+... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A deck of $2n$ cards numbered from $1$ to $2n$ is shuffled and n cards are dealt to $A$ and $B$ . $A$ and $B$ alternately discard a card face up, starting with $A$ . The game when the sum of the discards is first divisibl... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( k \\geq 1 \\) be an integer that divides 80. In a village of 81 dinosaurs, each dinosaur has a specific type of relationship with each other dinosaur (love, friendship, fraternity, kinship, etc.). There are exactly \\( k \\) di... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. The sequence \\(\\{a_{n}\\}\\) has consecutive terms \\(a_{n}\\) and \\(a_{n-1}\\) which are the roots of the equation \\(x^{2} - c_{n} x + \\left(\\frac{1}{3}\\right)^{n} = 0\\), and \\(a_{1} = 2\\). Find the sum of the first \\(2n\\)... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Uncle Zhang and Uncle Li have a combined age of 56 years. When Uncle Zhang was half Uncle Li's current age, Uncle Li’s age at that time was equal to Uncle Zhang’s current age. How old is Uncle Zhang now?"
},
{
"from": "assistan... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. It is known that \\(\\sin \\alpha = \\frac{3}{5}\\). Prove that \\(\\sin 25\\alpha\\) has the form \\(\\frac{n}{5^{25}}\\), where \\(n\\) is an integer, not divisible by 5."
},
{
"from": "assistant",
"value": "<|begin_of_th... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given a string S. The task is to find the first repeated character in it. We need to find the charac... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a circle and three lines \\(a, b, i\\), where \\(a\\) and \\(b\\) intersect the circle. Construct lines parallel to \\(i\\) that intersect the other two lines and the circle in such a way that the segment from one point of inters... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find all positive integer $n$ for which there exist real number $a_1,a_2,\\ldots,a_n$ such that $$ \\{a_j-a_i|1\\le i<j\\le n\\}=\\left\\{1,2,\\ldots,\\frac{n(n-1)}2\\right\\}. $$ "
},
{
"from": "assistant",
"value": ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Can the parameters \\(a, b, c\\) be chosen such that the following equality holds for all \\(x\\)?\n\n$$\n(x+a)^2 + (2x+b)^2 + (2x+c)^2 = (3x+1)^2 ?\n$$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay, so ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( x_{1}, x_{2}, \\cdots, x_{n} \\) be non-negative real numbers such that \\( x_{1} + x_{2} + x_{3} + \\cdots + x_{n} = a \\). Prove that \\( x_{1} x_{2} + x_{2} x_{3} + \\cdots + x_{n-1} x_{n} \\leq \\frac{1}{4} a^{2} \\)."
},... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A four-digit number has all distinct digits, and the sum of all the digits is 6. Additionally, the number is a multiple of 11. How many such four-digit numbers are there?\nA. 6\nB. 7\nC. 8\nD. 9"
},
{
"from": "assistant",
"... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Which one of the following bar graphs could represent the data from the circle graph?\n[asy] unitsize(36); draw(circle((0,0),1),gray); fill((0,0)--arc((0,0),(0,-1),(1,0))--cycle,gray); fill((0,0)--arc((0,0),(1,0),(0,1))--cycle,black); ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a tree with N vertices, numbered 1 through N.\n\nThe i-th of the N-1 edges connects the ver... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a circle that is tangent to the line $2x - y + 5 = 0$ at the point $M(-2, 1)$, and passes through the point $N(3, 2)$, find the equation of the circle."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nOkay... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Chris lies on Fridays, Saturdays, and Sundays, but he tells the truth on all other days. Mark lies on Tuesdays, Wednesdays, and Thursdays, but he tells the truth on all other days. On what day of the week would they both say: \"Tomorro... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. A traveler arrived on an island where 50 natives live, each of whom is either a knight or a liar. All natives stood in a circle, and each first named the age of their neighbor on the left, and then the age of their neighbor on the righ... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nProve (find $\\delta(\\varepsilon)$):\n\n$$\n\\lim _{x \\rightarrow-7} \\frac{2 x^{2}+15 x+7}{x+7}=-13\n$$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\n\nAlright, so I need to prove that the limit as x appro... | null | null | null | null | null | null | null | null | null | null |
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